Many applications have been developed in the framework of the \(f(R)\)  gravity such as early-time inflation [1]}, cosmological phases [2]}, [3]}, gravitational wave detection [4]}, [5]}, the stability of the solutions [6]}, [7]}, [8]} and other different issues [9]}. Interestingly, the duality between gravity and quantum field theory that has been introduced in [10]} and its applications considered in different theories and \(f(R)\)  gravity such as [11]}-[12]}. In addition, the different solutions of \(f(R)\)  gravity have been studied. Among these solutions, the authors in [13]} and [14]} deduced the static spherically symmetric solutions by involving a perfect fluid. The black hole solution with/without electric charge is presented in [15]}. Many analytic spherically symmetric solutions are derived in [16]}, [17]}, [18]}.
